The behavior of the free boundary near the fixed boundary for a minimization problem

DOI10.1007/S00526-006-0029-XzbMath1111.35135OpenAlexW2062371291MaRDI QIDQ859768

Carlos E. Kenig, Henrik Shahgholian, Aram L. Karakhanyan

Publication date: 18 January 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-006-0029-x

zbMATH Keywords

dam problemcontact pointsregularity of the free boundary

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Contact in solid mechanics (74M15) Flows in porous media; filtration; seepage (76S05) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35)

Related Items (11)

Boundary behaviour for a singular perturbation problem ⋮ Properties of the free boundary near the fixed boundary of the double obstacle problems ⋮ Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients ⋮ On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions ⋮ On the Lipschitz regularity of solutions of a minimum problem with free boundary ⋮ On the non-tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem ⋮ On a free boundary problem and minimal surfaces ⋮ Tangential touch between the free and the fixed boundary in a semilinear free boundary problem in two dimensions ⋮ On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem ⋮ Analysis of a free boundary at contact points with Lipschitz data ⋮ Branch points for (almost-)minimizers of two-phase free boundary problems

Cites Work

• On the regularity of a free boundary near contact points with a fixed boundary
• Partial regularity for a minimum problem with free boundary
• Regularity properties of a free boundary near contact points with the fixed boundary.
• Regularity of a free boundary with application to the Pompeiu problem
• Variational problems with two phases and their free boundaries
• Tangential Touch Between Free and Fixed Boundaries in a Problem from Superconductivity
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